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%I #11 Mar 07 2022 19:00:41
%S 175,1183,2259,5290,12969,21130,51820,70629,78090,79540,81818,129648,
%T 160224,169234,180908,228240,238574,249494,278628,332891,376335,
%U 383866,398650,399644,454090,550380,565200,683448,683604,694274,728895,754390,782110,809830,837550
%N Starts of runs of 3 consecutive lazy-tribonacci-Niven numbers (A352107).
%H Amiram Eldar, <a href="/A352109/b352109.txt">Table of n, a(n) for n = 1..10000</a>
%e 175 is a term since 175, 176 and 177 are all divisible by the number of terms in their maximal tribonacci representation:
%e k A352103(k) A352104(k) k/A352104(k)
%e --- ---------- ---------- ------------
%e 175 11111110 7 25
%e 176 11111111 8 22
%e 177 100100100 3 59
%t t[1] = 1; t[2] = 2; t[3] = 4; t[n_] := t[n] = t[n - 1] + t[n - 2] + t[n - 3]; trib[n_] := Module[{s = {}, m = n, k}, While[m > 0, k = 1; While[t[k] <= m, k++]; k--; AppendTo[s, k]; m -= t[k]; k = 1]; IntegerDigits[Total[2^(s - 1)], 2]]; lazyTriboNivenQ[n_] := Module[{v = trib[n]}, nv = Length[v]; i = 1; While[i <= nv - 3, If[v[[i ;; i + 3]] == {1, 0, 0, 0}, v[[i ;; i + 3]] = {0, 1, 1, 1}; If[i > 3, i -= 4]]; i++]; i = Position[v, _?(# > 0 &)]; If[i == {}, False, Divisible[n, Total[v[[i[[1, 1]] ;; -1]]]]]]; seq[count_, nConsec_] := Module[{tri = lazyTriboNivenQ /@ Range[nConsec], s = {}, c = 0, k = nConsec + 1}, While[c < count, If[And @@ tri, c++; AppendTo[s, k - nConsec]]; tri = Join[Rest[tri], {lazyTriboNivenQ[k]}]; k++]; s]; seq[30, 3]
%Y Cf. A352103, A352104.
%Y Subsequence of A352107 and A352108.
%Y A352110 is a subsequence.
%Y Similar sequences: A154701, A328206, A328210, A328214, A330932, A331087, A333428, A334310, A331822, A342428, A344343, A351716, A351721, A352091.
%K nonn,base
%O 1,1
%A _Amiram Eldar_, Mar 05 2022